**Subject :**Electrical Machines II (AC Machines)

**Unit :**Synchronous motor

## Equivalent circuit model and phasor diagram of a synchronous motor

**Equivalent circuit model of a synchronous motor:**

*Fig 1: Equivalent circuit
*

The equivalent-circuit model for one armature phase of a cylindrical rotor three phase synchronous motor is shown in Fig. 1 exactly similar to that of a synchronous generator except that the current flows in to the armature from the supply. All values are given per phase. Applying Kirchhoff’s voltage law to Fig.1

Combining reactances, we have

Substituting the above equations we have,

where:

R_{a} = armature resistance (Ω/phase)

X_{l} = armature leakage reactance (Ω /phase)

X_{s} = synchronous reactance (Ω /phase)

Z_{s} = synchronous impedance (Ω /phase)

V_{T} = applied voltage/phase (V)

I_{a} = armature current/phase(A)

**Phasor diagram of a synchronous motor:**

A phasor diagram shown in Fig. 2, illustrates the method of determining the counter EMF which is obtained from the phasor equation;

The phase angle δ between the terminal voltage V_{T} and the excitation voltage E_{f} in Fig. 2 is usually termed the torque angle. The torque angle is also called the load angle or power angle.